Plasma and Fusion Research: Regular Articles

Volume 13, 3402059 (2018)

TSC Simulation of Transient CHI in New Electrode Configuration
on QUEST∗)
Kengoh KURODA, Roger RAMAN1) , Stephen C. JARDIN2) , Masayuki ONO2) andKazuaki HANADA
Kyushu University, Kasuga, Fukuoka 816-8580, Japan
1)
University of Washington, Seattle, WA, 98195, USA
2)
Princeton Plasma Physics Laboratory, Princeton, NJ, 08543, USA(Received 27 December 2017 / Accepted 15 April 2018)
In QUEST, transient Coaxial Helicity Injection (CHI) has now been implemented using a new electrodeconfiguration in which the CHI insulator is not part of the vacuum boundary. In this paper, for the first time,
suitable conditions for generation of the CHI-produced toroidal current in the QUEST vessel configuration were
investigated using the Tokamak Simulation Code (TSC). The simulation results show that the configuration inwhich the biased electrode is located farther away from the injector flux coil requires higher currents in theinjector coil to generate the required injector flux. Additionally, energizing a lower inboard poloidal field coiland possibly lowering the electrode plate closer to the injector flux coil may be necessary to improve injector flux
shaping to permit a configuration that is more favorable for inducing flux closure.
c 2018 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: CHI, TSC, non-inductive current drive, spherical tokamak, ECH
DOI: 10.1585/pfr.13.3402059

1. Introduction
Transient Coaxial Helicity Injection (CHI) is a useful method to generate plasma current without the use of asolenoid in a low aspect ratio spherical tokamak (ST) device as it has the advantages of low construction cost andhigh plasma beta which is desired in a future fusion reactor.
On the HIT-II experiment at the University of Washington,
the method referred to as transient CHI was developed,
which generated toroidal plasma currents accompanied by
the formation of closed-flux surfaces. These plasmas were
subsequently ramped up to 290 kA using inductive drivethat consumed less solenoid flux compared to discharges
without CHI start-up [1]. The method was further developed on the NSTX device at the Princeton Plasma Physics
Laboratory (PPPL) where a CHI produced plasma currentof about 200 kA was ramped up to 1 MA by using only
65 % of the solenoid flux of a discharge with full inductive
drive [2].
In the mid-size ST device, QUEST [3,4], we have now
implemented transient CHI capability through a collaborative research with the University of Washington and PPPL
[5]. The main objectives of this experiment are the demonstration of generating CHI plasma using a new, much morereactor-relevant, electrode configuration and the investigation of the eﬃciency of CHI coupling to electron cyclotron
resonance heating (ECH). The new electrode configuration, shown in Fig. 1, is designed to facilitate easier imauthor’s e-mail: kuroda@triam.kyushu-u.ac.jp∗) This article is based on the presentation at the 26th International Toki
Conference (ITC26).

plementation of CHI in future fusion reactors [6]. In thisconfiguration the insulator is sandwiched between the bias
electrode plate and the lower divertor plate, and it is notpart of the vessel vacuum boundary as in NSTX and HITII. In this configuration, it is easier to shield the insulator
from neutrons in a burning plasma device. Additionally,transient CHI plasmas have low intrinsic electron temperature, and they must be heated to the 1 keV temperature
range for coupling to other non-inductive current sustainment methods [7]. ECH is a very powerful tool for heating
low-temperature plasmas. Demonstrating electron heatingof a transient CHI target using the high power 28 GHz ECH
system on QUEST is an important objective [8].
In experiments thus far, we have achieved reliable gas
breakdown [5] and good CHI plasma evolution. Demonstration of the formation of closed-flux surfaces is the next
important objective. In support of this objective, the Tokamak Simulation Code (TSC) [9, 10] was used to understand the required PF coil programming to achieve desirable toroidal current evolution into the QUEST vessel thatis favorable for a formation of flux closure.
The TSC code was developed at PPPL [9, 10] for simulating inductive tokamak plasma discharges. It simulates
axisymmetric and free-boundary tokamak plasmas. In thecode, information related to vessel and poloidal field coil(PF) parameters need to be provided as input. The required
information is the vessel and coil shape and size as wellas the resistance of all conductors. For the PF coils, thenumber of turns in the coil also needs to be provided. In

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Table 1 Simulated discharge conditions.

Fig. 1 CHI components on QUEST – the biased CHI electrodeshown in red is positioned above the lower divertor plate.
(b) Photo of CHI electrodes in QUEST. Reprinted withpermission from [5].

addition, basic information about the plasma parameters
are included. For simulating CHI discharges, the plasma
electron temperature is used to calculate the Spitzer resistivity. The code then solves the MHD/Maxwell’s equations
and the circuit equations for the Poloidal Field coils. The
region inside a rectangular computational grid is solved
with finite diﬀerence equations, and a Green’s function approach extends the solution to infinity.

2. TSC Simulations
In these first simulations of the QUEST CHI configuration, to touch base with previous such simulations for
NSTX [11], we first studied the impact of moving the CHI
electrodes farther away from the injector flux coil (as on
QUEST), vs. closer positioning of the electrodes to theinjector flux coil (as on NSTX). Five configurations werestudied, as described in Table 1.
In Table 1, the ‘N’ electrode location refers to the electrode plates located closer to the injector flux coil, whilethe ‘Q’ configuration refers to the plates being lifted up

from the injector flux coil and located farther away fromthe coil, as on QUEST. A comparison of the lower vesselboundary on Figs. 2 and 3 shows the diﬀerence between
the ‘N’ and ‘Q’ configurations. In Table 1, the terms ‘Low’
and ‘Lift up’ are used to identify these two configurations.
The injector flux coil current is the current driven in theinjector coil PF5-2 to generate the required injector flux.
In configuration N1, starting from an initial value, the current in the injector coil is rapidly ramped down in time,
while in configuration N2 the coil current is held constantin time. In the ‘Q’ configurations the electron temperatureand the applied voltage are varied, as shown in Table 1.
The injector flux is the magnitude of poloidal injector fluxthat connects the two electrodes, electron temperature is
the temperature of the plasma used in the simulations, andthe injector voltage is the voltage applied to the electrodes.
In all cases, the toroidal coil current is 800 kA.
TSC was developed primarily for simulating axisymmetric inductive plasmas. While it has been used to support CHI experimental activities, it is not meant to exactly
duplicate the experiment. Instead it is used as a guide forexperiments to understand how the evolving CHI plasma
can be controlled by appropriate choice of the poloidal
field coil currents. Thus, TSC cannot be used to determine
the exact value of closed flux current that can be generated
in a given CHI configuration, but it can help one gain anunderstanding of configurations that can likely help optimize closed flux formation. The detailed aspects of closed
flux current generation require a 3-d resistive MHD codesuch as NIMROD [12, 13]. Specifically, for QUEST, these
initial TSC simulations have already helped us identify theneed for energizing an additional PF coil to improve the
CHI plasma evolution. In simulating QUEST CHI discharges, the vessel model is simplified to reproduce themost important parameters needed to model the poloidal
flux evolution. These are the physical location of the CHI
electrode area in relation to the PF coils, and the PF coiland vessel parameters. To have confidence that these simulations are meaningful, we also simulated a case in which
the vessel configuration looks similar to the NSTX vessel
configuration, and a configuration that has been previously
studied using the TSC code [11]. In Table 1, these are3402059-2

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Fig. 3 Simulated results for configurations Q1-Q3 in which theelectron temperature is changed, (a) flux evolution, (b)time plot of loop voltage at location X.

Fig. 2 Simulated results for cases N1 and N2, (a) - (c); flux evolution at three diﬀerent times and the poloidal flux at z =0. Current is driven in PF coils shown in red color. “d” isthe flux footprint width. (d), (e); time plot of injector current and loop voltage at the two locations marked with an
X in (a) - (c), (f); programed time plot of PF5-2 injector
flux coil current.

identified with labels ‘N’ and ‘Q’ to represent the NSTX
and QUEST-like configurations. The simulation area covers the region of the PF coils and the vacuum vessel. This
entire area is modeled as small rectangular grids with across-section of 4 cm × 4 cm each. At each of these grid
locations the resistivity of the region is specified. To sim-

ulate CHI, in the lower part of the vessel a small region
corresponding to the approximate location of the vacuum
gap between the anode and cathode electrodes is specified
to have very high resistance, like that of an insulator. A
yellow rectangle on the lower part of the vessel in Fig. 1 (a)shows the insulator gap. The TSC model requires the needfor a second insulator to avoid current from flowing along
the QUEST vessel walls. In this model, this is located on
the top of the vessel as shown by another yellow rectangle
as in NSTX. The injector flux is located on either side of
the high resistance gap on the lower part of the vessel, in
which voltage is applied to either side of the gap. The applied voltage causes currents to flow along the initial vacuum flux that is present on either side of this gap, whichadequately simulates the actual current flowing between
the bias and ground electrodes. The electron temperature
in Table 1 is used to prescribe a resistivity profile for themagnetic flux region. As currents flow along these fieldlines, a J × B force is generated that causes the poloidal
flux to evolve into the vessel region. Currents driven in
the PF coils then determine the shape of the evolving CHI
plasma discharge, as shown in Figs. 2 and 3.
In CHI terminology, the average distance between thetwo injector flux footprints on the electrodes is the flux
footprint width, ‘d’. While the vacuum gap distance setsa lower value for the injector flux footprint width, the actual value for ‘d’ is determined by how much the injector
flux footprint itself is spread out on the electrode surface,
as shown in Fig. 2 (a). By increasing the current in the coils

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adjacent to the main injector coil, the value of ‘d’ can be
reduced and made narrower.
Figure 2 shows the simulated results for configuration
N1. In this case, the CHI electrode is located closer to theinjector flux coils. The initial PF configuration in (a), at t
= 0 s, shows the shape of the vacuum injector flux. 5 mWb
of injector flux forms the injector current path, and it isgenerated by using only 0.4 kA of current in the injector
flux coil PF5-2. The Peak injector voltage is 120 V. The
time-dependent voltage for all cases is applied in the sameway. It increases from 0 V at t = 0 ms to a peak value at
0.2 ms. It is held at the peak value for 0.1 ms, then it isdecreased back to 0 V at t = 0.7 ms. With the applicationof the voltage, the injector current flows along helical fieldlines formed by the combination of the injector flux and thetoroidal field. With increasing injector current, as shown in(b), the injector flux expands into vessel when the interaction force between the injector current and toroidal field
generated by the injector current exceeds the tension of theinjector flux field lines [14]. After the injected flux fills
the vessel, the time plot (d) shows that the injector current
decreases rapidly because the injector voltage is reduced.
This causes the injected flux to decay in time, inducing a
positive loop voltage in the plasma region. The plot of theloop voltage (e) shows that it is negative as poloidal flux is
injected into the vessel, but later in time becomes positive
as the injected flux decays. Generation of closed flux in
TSC simulations of CHI is due to this positive loop voltage generation by the decaying injected flux.
The conditions for case N2 are the same as the conditions in case N1 except that the current in the PF5-2 coil is
kept constant in time, whereas for case N1 it is decreased to
0 Amp after the flux injection phase, as shown in Fig. 2 (f).
However, the results for case N2 show similar flux evolution and closed flux formation as N1. This suggests that the
rapidly reducing injector current is more important than therole of PF5-2 coil current ramp-down for inducing a positive loop voltage that is necessary in the TSC model for
inducing the initial flux closure.
To clarify, in comparing cases N1 and N2, we notethat there are two loop voltages. First is the loop voltage
produced due to the changing current in the injector coil.
In case N2, this is zero because the current in the injector
coil PF5-2 is not changed in time. In case N1, it is positive
because the current in this coil is decreasing in time. But
this does not seem to result in significantly increased initialflux closure probably because the coil is far away from thecentral plasma region. Second is the loop voltage inducedby the decaying open poloidal flux that has already been
injected into the vessel during the CHI start-up process.
For this flux, the action of driving open-field line current
provides the J × B force necessary to keep it stretched inside the vessel. Once this open field line current drive has
been removed (by rapidly reducing the injector voltage),then this injected flux can no longer remain in the vessel,
and it will start to pull back into the injector. It is the decayof this flux that generates the positive loop voltage needed
for flux closure. If the injector flux footprint width is narrow, then that would make it much more diﬃcult for thepoloidal flux in the vessel to fully pull back into the injector region, and a greater amount of the injected open flux
can close to form a closed flux configuration.
In cases Q1-3, the bias electrode is lifted up to the location corresponding to that on QUEST, as shown in Fig. 3.
In this electrode configuration, the PF5-2 coil current isincreased to 3.0 kA to produce 25 mWb of injector flux.
Because the region of the high magnetic flux density is atlarger major radius for this configuration, relatively highcurrents are also needed in the PF4-3 and PF5-1 coils asotherwise the injector flux is spread-out over a large electrode area making the injector flux footprint width large.
Driving currents in these coils causes the injector flux tobe more concentrated near the gap region that is above
the PF5-2 coil. Under these conditions the injector flux
is more concentrated near the electrode gap region, as forcase N, and flux closure is also seen in this configuration,
as shown in Fig. 3. These cases require less voltage because, in general, the injector flux can be thought of as
shorting the electrodes. So with other factors remaining
the same, a higher value of the injector flux requires lessvoltage to obtain a given value of injector current that is
consistent with plasma growth that fills the vessel [11]. It
is also useful to note that the magnitude of the toroidal current is less than for the cases in Fig. 2. This is because theattainable toroidal current is proportional to the ratio of thetoroidal flux to the injector flux, but this toroidal current
does not say how much closed flux current can be achievedin a given CHI configuration as discussed in Ref. [2].
Figure 3 shows the results for cases Q1, Q2 and Q3,
in which the electron temperatures are 200 eV, 100 eV and
50 eV, respectively. At lower electron temperature, increased plasma resistivity would allow the injected flux todecay faster and this induces a higher loop voltage. This
result suggests that although a lower electron temperature
may be more suitable for inducing closed flux formationin TSC simulations, the resulting plasma will also decay
away faster, so it will be necessary to increase the plasma
electron temperature by some other means (such as forexample by ECH heating) to confine the CHI produced
closed flux for long durations for eventually coupling the
CHI target to other non-inductive current drive methods.
Figure 4 is a plot of the CHI produced toroidal current for all cases. Here it is important to note that mostof the CHI produced current in these simulations flows on
open field lines. Therefore, the term toroidal current, instead of plasma current, is used to make this distinction
clear. The important parameter is the peak toroidal current,
which occurs at about 0.7 ms. The persistent toroidal current in these simulations past about 1 ms is not particularlyof interest to this study, as they have not been adequately
modelled in these initial simulations and will be the subject of future work. For cases Q1 to Q3, the peak toroidal

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Fig. 4 Time plot of CHI produced toroidal current for cases, N12, Q1-3.

current in all cases is much less than for the NSTX-like
case, suggesting that QUEST CHI research can benefit if
the electrode location is lowered so that it is closer to thePF5-2 coil or possibly through the addition of a new PF
coil that is positioned to be closer to the electrode plate.

3. Summary
The first simulations have provided useful guidance
for transient CHI experiments on QUEST. First, the results
show that in the QUEST-like configuration in which theelectrode plate is farther away from the injector coil it may
be quite important to energize the PF4-3 coil in order toproduce a suﬃciently narrow injector flux footprint width
so as to induce flux closure. Without the use this coil, theinjector flux is simply spread out too widely along the electrode surface, which makes is easy for the injected flux topull back into the injector after the injector current is reduced to zero.
Second, closer positioning of the electrode plate to thePF5-2 coils allow the injector flux footprints to be moreeasily controlled. This would suggest the need for somelowering of the electrode plate combined with the use of
CHI-specific injector coil or coils as a future modification
to the CHI system design on QUEST.
The simulations also show that, in the 2d scenario ofTSC, ramping down the injector coil current does not seemto be an important factor for inducing flux closure dur-ing the very early phase of flux closure. Finally, although
flux closure seems easier at lower electron temperatures,
the need for a high electron temperature plasma for futuresustained non-inductive operation means that a high power
ECH system may be necessary to support CHI studies.
As noted in Section 2 and due to the limitations of thepresent TSC model, it is not useful to make quantitative
comparisons of closed flux generation at this stage in thesevery first simulations of the CHI configuration in QUEST.
In addition, the induced loop voltage is not the only mechanism for closed flux generation in CHI plasmas, as indicated by related simulations for the NSTX geometry with
the NIMROD code [12, 13].

Acknowledgments
This work is supported by Japan / U. S. Cooperationin Fusion Research and Development, NIFS Collaboration Research Program (NIFS17KUTR130), the Collaborative Research Program of RIAM, Kyushu University (international collaboration frame work No.8 in 2017) and a
Grant-in-Aid for JSPS Fellows (KAKENHI Grant Number 16H02441, 24656559). This work is supported by US
DOE under the Contracts DE-FG02-99ER54519 and DEAC02-09CH11466.
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